Projective Geometries

Action at a Distance

Now ths statement might seem counterproductive to the ideas of projective geometry but please bear with me.

In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. This term was used most often with early theories of gravity and electromagnetism to describe how an object could "know" the mass (in the case of gravity) or charge (in electromagnetism) of another distant object.

According to Albert Einstein's theory of special relativity, instantaneous action-at-a-distance was seen to violate the relativistic upper limit on speed of propagation of information. If one of the interacting objects were suddenly displaced from its position, the other object would feel its influence instantaneously, meaning information had been transmitted faster than the speed of light.

Test of the Quantenteleportation over long distances in the duct system of Vienna Working group Quantity of experiment and the Foundations OF Physics Professor Anton Zeilinger

Quantum physics questions the classical physical conception of the world and also the everyday life understanding, which is based on our experiences, in principle. In addition, the experimental results lead to new future technologies, which a revolutionizing of communication and computer technologies, how we know them, promise.

In order to exhaust this technical innovation potential, the project "Quantenteleportation was brought over long distances" in a co-operation between WKA and the working group by Professor Anton Zeilinger into being. In this experiment photons in the duct system "are teleportiert" of Vienna, i.e. transferred, the characteristics of a photon to another, removed far. First results are to be expected in the late summer 2002.

One of the first indications to me came as I looked at the history in regards to Klein's Ordering of Geometries. Now I must admit as a layman I am very green at this understanding but having jumped ahead in terms of the physics involved, its seems things have been formulating in my head, all the while, this underatnding in terms of this "order" has been lacking.

In Euclidean geometry, the basic notions are distances and angles. The transformations that preserve distances and angles are precisely the rigid motions. Effectively, Klein's idea is to reverse this argument, take the group of rigid motions as the basic object, and deduce the geometry. So a legitimate geometric concept, in Euclidean geometry, is anything that remains unchanged after a rigid motion. Right-angled triangle, for example, is such a concept; but horizontal is not, because lines can be tilted by rigid motions. Euclid's obsession with congruent triangles as a method of proof now becomes transparent, for triangles are congruent precisely when one can be placed on top of the other by a rigid motion. Euclid used them to play the same role as the transformations favored by Klein.

In projective geometry, the permitted transformations are projections. Projections don't preserve distances, so distances are not a valid conception projective geometry. Elliptical is, however, because any projection of an ellipse is another ellipse.

So spelt out here is one way in which this progression becomes embedded within this hisotry of geometry, while advancing in relation to this association I was somewhat lifted to question about Spooky action at a distance. WEll if such projective phase was ever considered then how would distance be irrelevant(this sets up the idea then of probabilistic pathways and Yong's expeirment)? There had to be some mechanism already there tht had not been considered? Well indeed GHZ entanglement issues are really alive now and such communication networks already in the making. this connection raised somewhat of a issue with me until I saw the the phrase of Penrose, about a "New Quantum View"? Okay we know these things work very well why would we need such a statement, so I had better give the frame that help orientate my perspective and lead to the undertanding of spin.



Now anywhere along the line anyone can stop such erudication, so that these ideas that I am espousing do not mislead. It's basis is a geometry and why this is important is the "hidden part of dirac's mathematics" that visionization was excelled too. It is strange that he would not reveal these things, all the while building our understanding of the quantum mechanical nature of reality. Along side of and leading indications of GR, why would not similar methods be invoked as they were by Einstein? A reistance to methodology and insightfulness to hold to a way of doing things that challenegd Dirac and cuased sleepless nights?



Have a look at previous panel to this one.

While indeed this blog entry open with advancements in the Test in Vienna, one had to understadn this developing view from inception and by looking at Penrose this sparked quite a advancement in where we are headed and how we are looking at current days issues. Smolin and others hod to the understnding f valuation thta is expeirmentally driven and it is not to far off to se ehosuch measure sare asked fro in how we ascertain early universe, happening with Glast determinations.

Quantum Cryptography

Again if I fast forward here, to idealization in regards to quantum computational ideas, what value could have been assigned to photon A and B, that if such entanglement states recognize the position of one, that it would immediately adjust in B?

Spooky At any Speed

If a pair of fundamental particles is entangled, measuring an attribute of one particle, such as spin, can affect the second particle, no matter how far away. Entanglement can even exist between two separate properties of a single particle, such as spin and momentum. In principle, single particles or pairs can be entangled via any combination of their quantum properties. And the strength of the quantum link can vary from partial to complete. Researchers are just beginning to understand how entanglement meshes with the theory of relativity. They have learned that the degree of entanglement between spin and momentum in a single particle can be affected by changing its speed ("boosting" it into a new reference frame) but weren't sure what would happen with two particles.

So there is this "distance measure" here that has raised a quandry in my mind about how such a projective geometry could have superceded the idea of "spooky things" and the issues Einstein held too.

So without understanding completely I made a quantum leap into the idealization in regards to "logic gates" as issues relevant to John Venn and introduced the idea around a "relative issues" held in my mind to psychological methods initiated by such entanglement states.

As far a one sees here this issue has burnt a hole in what could have transpired within any of us that what is held in mind, ideas about geomtires floated willy Nilly about. How would such "interactive states" have been revealled in outer coverings.

The Perfect Fluid

Again I am fstforwding here to help portray question insights that had been most troubling to me. If suych supersymmetrical idealizations arose as to the source and beginning of existance how shall such views implement this beginning point?

So it was not to unlikely, that my mind engaged further problems with such a view that symmetry breaking wouldhad tohave signalled divergence from sucha state of fluid that my mind encapsulated and developed the bubble views and further idealizations, about how such things arose from Mother.

What would signal such a thing as "phase transitions" that once gauged to the early universe, and the Planck epoch, would have revealled the developing perspective alongside of photon developement(degrees of freedom) and released information about these early cosmological events.

So I have advance quite proportinately from the title of this Blog entry, and had not even engaged the topological variations that such a leading idea could have advanced in our theoretcical views of Gluonic perceptions using such photonic ideas about what the tragectories might have revealled.

So indeed, I have to be careful here that all the while my concepts are developing and advanced in such leaps, the roads leading to the understanding of the measure here, was true to form and revalled issues about things unseen to our eyes.

It held visionistic qualities to geometric phases that those who had not ventured in to such entanglement states would have never made sense of a "measure in the making." It has it's limitation, though and why such departures need to be considered were also part of my question about what had to come next.

Emergence= Phase Transitions of Symmetry?

Witten said:

One thing I can tell you, though, is that most string theorist's suspect that spacetime is a emergent Phenomena in the language of condensed matter physics.

Part of the difficulty was realizing that the end result of a current depiction of the universe, and the reality around us now, had led us to assumption discrete manifestations of a earlier prospective universe. From that early universe, until now.

In 1877 Boltzmann used statistical ideas to gain valuable insight into the meaning of entropy. He realized that entropy could be thought of as a measure of disorder, and that the second law of thermodynamics expressed the fact that disorder tends to increase. You have probably noticed this tendency in everyday life! However, you might also think that you have the power to step in, rearrange things a bit, and restore order. For example, you might decide to tidy up your wardrobe. Would this lead to a decrease in disorder, and hence a decrease in entropy? Actually, it would not. This is because there are inevitable side-effects: whilst sorting out your clothes, you will be breathing, metabolizing and warming your surroundings. When everything has been taken into account, the total disorder (as measured by the entropy) will have increased, in spite of the admirable state of order in your wardrobe. The second law of thermodynamics is relentless. The total entropy and the total disorder are overwhelmingly unlikely to decrease

Now the apparent contradiction is to understand that when the views are taken to those small spaces, reductionistic features of a discrete nature have forced us to consider the building blocks of matter, but at the same time, something else makes it's way into our views that would have been missed had you not realized that the space contains a lot of energy?

To build this symmetrical and simple model of elegance, you needed some model, some framework in which to consider the distant measure here would be ultimately derived from the blackhole and it's dynamics? The simple solution would help you recognize that any massless particle emitted from this state, would automatically signal the closest source of consideration that any of us could have imagined.

Even Smolin, recognized the Glast determinations. Why I have said, that Smolin could not have gotten any closer then what is surmised from the origination of emission from the blackhole consideration?

HIgher Dimensions Without the Geometry?

In Illusions and Miracles I became concerned with what the mind's capabilties which could encounter fifth dimensional views. That such examples were needed, and found in relation to Thomas Banchoff.

Having understood the early development from Euclidean perspective, our furthered evolutionary developement of the geometries, were gained by moving beyond the fifth postulate. I became comfortable with a dynamical realization about our universe(Omega), and about the idealization of curvature in dynamical fields of supergravity.

I made the statement that GR is reduced from the higher geometries and along with that view the understanding that things existed in earliers states of being. Robert Laughlin's views of complexity and symmetry breaking would reveal to me, that the matter states of form, were derived from "other states of existance". This is a fundamental realization of higher dimensional attributes revealled in the topologies/geometries. So from higher, and the continuity of, topological considerations to the firmly fixed realms of geometries in the forms? So from early universe to now, what views allow us to consider that symmetical breaking that has gone through phase transitions, to get from the planck epoch phase of our universe to today?

Having come in contact with a new type of thinking in the realm of the geometries, it became very important to me to understand how this could have manifested early in our historical background? I followed it through GR in order for this to make sense, I continued to move and consider the higher dimensional relevance new models might use in their move to the abstracts realms of thinking.

Here I would interject the realization of string theory, and ask why such a rejection mathematically, would dimiss the subject of strings based on this dimensional realization, and then quickly disperse, string's relevance because of the higher dimensional significance brought to bear on the attribtues of the minds capabilties? Part of the develpement of the brains compacity was the realization that such images produced(higher topological math forms), could indeed symmetryically break to forms within the world. Forms within mind, that could lead to solification in the math? When is a Pipe a Pipe?:)

This is what had troubled me most, noting Peter Woit's rejection of the value of his "anti" campaign of string theory evolution. Maybe, it was more then the idea of the subject and it's established views that he felt were as much part of the illusion as any other theory, that found itself unscientifically determined? Based on the constructs string theory developed? Maybe it was the funding biased felt towards this subject, and lack of, somewhere else. We wouldn't know this, because he had no alternative?

GR Reduced From Higher Dimensions?

Earlier in my blog, I posted a subject called the Classical discription of the quantum world

Now it was a big leap of faith on my part that I saw these events as distilliations of a larger and more dynamic universe that cooled to proportionl views that I had related in that post. But now, this might be rejected based on the work done on this cosmological observatory, that is not mirrored from a larger proportional view of that early universe? What does this mean?

If planck epoch arises to expansitory features revealled in our cosmos, then, early universe detection is a valid assumption of this earlier design?

That the comments posted by Arun in the blog entitled crackpotism, contrasted to my statement, has much more discussion behind it to consider.

Arun said: So, string theory embraces both General Relativity and not-General Relativity!!!! In other words, string theory says nothing definite.

Plato said: And about Arun's comment about GR. Phase transitions would be reduced holographcally from higher dimensions( the standard model would have been decribed from earlier states ), would finally show up there?:)

If one did not recognize earlier states of existence and just accepted the cosmological playground sight seen, it always existed in this form then:) That is, if we take the standard set by observation:)

I for one thought, topological considerations would have been formulated from earlier cosmic designs, but apparently this might have been subject to scrutiny, and thought out. Rejection of the soccer ball design as well?:)

So I guess I'll get to it here and post the following for consideration.

The significance of the largest scale CMB fluctuations in WMAP:

Now of course, we must remember that the way in which I am looking at this universe is that we see it in it's earlier state, as spread out(higher dimensional attributes), much like we see the discription of the early computerize version shown here .

Computerized Model of Andrey Kravtsov.

The current state of the universe, globally, would be a derived from some view point that represents the current shape and size of the universe. Represents its current age, to design? At least, this is what would have been derived from the sources I am considering in light of the assumption I am making, has some realistic version, that would hold to such spherical considerations. Hold on Peter Woit:)



So such a point although subject to these phase transitions are in the end understood on the other end of the scale of consideration from that early universe to today. To what passes us by? We are attempting to measure at this point in time, what "rings true" through all of us?:)

Bubble Nucleation

Based on the no boundary proposal, I picture the origin of the universe, as like the formation of bubbles of steam in boiling water. Quantum fluctuations lead to the spontaneous creation of tiny universes, out of nothing. Most of the universes collapse to nothing, but a few that reach a critical size, will expand in an inflationary manner, and will form galaxies and stars, and maybe beings like us.

The images produce here of bubble formation are most pleasing to me, about what could have emerge from that early universe. If stringy components were evident and cosmic clumping rvealed as in previous post then how would such images lead to bubble nucleations as stringy cosmological patterns?

For such ideas to emerge in thinking there had to be a time when such conditions were conducive to bubble nucleation? Such energy considerations had to provide for these considerations to emerge so. How so?

First-order phase transitions (illustrated below) occur through the formation of bubbles of the new phase in the middle of the old phase; these bubbles then expand and collide until the old phase disappears completely and the phase transition is complete.



During a first-order phase transition, the matter fields get trapped in a `false vacuum' state from which they can only escape by nucleating bubbles of the new phase, that is, the `true vacuum' state.





G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1). Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature

In order for such thinking to produce the cosmos then we would have to understand its early conditions.

Physically, the effect can be interpreted as an object moving from the "false vacuum" (where = 0) to the more stable "true vacuum" (where = v). Gravitationally, it is similar to the more familiar case of moving from the hilltop to the valley. In the case of Higgs field, the transformation is accompanied with a "phase change", which endows mass to some of the particles.